泛q模拟Bannai-Ito代数的基

Bases for Universal q-analog Bannai-Ito Algebra

令C代表复数域,q是C中一个非零元素,且满足q^4≠1.定义一个结合C-代数Δ=Δ_q,其生成元为A,B,C,且qBC+q^(-1)CB-A,qCA+q^(-1)AC-B,qAB+q^(-1)BA-C都为Δ的中心元,称Δ为泛q-模拟Bannai-Ito代数.给出了Δ作为C-向量空间的2组基.

Let Cdenote a field,and fix a nonzero q∈Csuch that q4≠1.We define an associative C-algebraΔ=Δqby generators A,B,Cand relations asserting that each of qBC＋q-1CB-A,qCA＋q-1AC-B,qAB＋q-1BA-Cis central inΔ.We callΔthe universal q-analog Bannai-Ito algebra.In this paper,we give two bases for the C-vector spaceΔ.